This invention relates to interferometers, e.g., linear and angular displacement measuring and dispersion interferometers, that measure linear and angular displacements of a measurement object such as a mask stage or a wafer stage in a lithography scanner or stepper system, and also interferometers that monitor wavelength and determine intrinsic properties of gases.
Displacement measuring interferometers monitor changes in the position of a measurement object relative to a reference object based on an optical interference signal. The interferometer generates the optical interference signal by overlapping and interfering a measurement beam reflected from the measurement object with a reference beam reflected from a reference object.
In many applications, the measurement and reference beams have orthogonal polarizations and different frequencies. The different frequencies can be produced, for example, by laser Zeeman splitting, by acousto-optical modulation, or internal to the laser using birefringent elements or the like. The orthogonal polarizations allow a polarizing beam-splitter to direct the measurement and reference beams to the measurement and reference objects, respectively, and combine the reflected measurement and reference beams to form overlapping exit measurement and reference beams. The overlapping exit beams form an output beam that subsequently passes through a polarizer. The polarizer mixes polarizations of the exit measurement and reference beams to form a mixed beam. Components of the exit measurement and reference beams in the mixed beam interfere with one another so that the intensity of the mixed beam varies with the relative phase of the exit measurement and reference beams.
A detector measures the time-dependent intensity of the mixed beam and generates an electrical interference signal proportional to that intensity. Because the measurement and reference beams have different frequencies, the electrical interference signal includes a “heterodyne” signal having a beat frequency equal to the difference between the frequencies of the exit measurement and reference beams. If the lengths of the measurement and reference paths are changing relative to one another, e.g., by translating a stage that includes the measurement object, the measured beat frequency includes a Doppler shift equal to 2 vnp/λ, where v is the relative speed of the measurement and reference objects, λ is the wavelength of the measurement and reference beams, n is the refractive index of the medium through which the light beams travel, e.g., air or vacuum, and p is the number of passes to the reference and measurement objects. Changes in the phase of the measured interference signal correspond to changes in the relative position of the measurement object, e.g., a change in phase of 2π corresponds substantially to a distance change L of λ/(2 np). Distance 2L is a round-trip distance change or the change in distance to and from a stage that includes the measurement object. In other words, the phase Φ, ideally, is directly proportional to L, and can be expressed asΦ=2 pkL cos2 θ  (1)for a plane mirror interferometer, e.g., a high stability plane mirror interferometer, where
  k  =            2      ⁢      π      ⁢                          ⁢      n        λ  and θ is the orientation of the measurement object with respect to a nominal axis of the interferometer. This axis can be determined from the orientation of the measurement object where Φ is maximized. Where θ is small, Equation (1) can be approximated byΦ=2 pkL(1−θ2)  (2)
Unfortunately, the observable interference phase, {tilde over (Φ)}, is not always identically equal to phase Φ. Many interferometers include, for example, non-linearities such as those known as “cyclic errors.” The cyclic errors can be expressed as contributions to the observable phase and/or the intensity of the measured interference signal and have a sinusoidal dependence on the change in for example optical path length 2 pnL. A first order cyclic error in phase has, for example, a sinusoidal dependence on (4πpnL)/λ and a second order cyclic error in phase has, for example, a sinusoidal dependence on 2(4πpnL)/λ. Higher order cyclic errors can also be present as well as sub-harmonic cyclic errors and cyclic errors that have a sinusoidal dependence of other phase parameters of an interferometer system comprising detectors and signal processing electronics.
There are in addition to the cyclic errors, non-cyclic non-linearities or non-cyclic errors. An example of a source of a non-cyclic error is the diffraction of optical beams in the measurement paths of an interferometer. Non-cyclic error due to diffraction has been determined for example by analysis of the behavior of a system such as found in the work of J.-P. Monchalin, M. J. Kelly, J. E. Thomas, N. A. Kurnit, A. Szöke, F. Zernike, P. H. Lee, and A. Javan, “Accurate Laser Wavelength Measurement With A Precision Two-Beam Scanning Michelson Interferometer,” Applied Optics, 20(5), 736-757, 1981. A second source of non-cyclic errors is the effect of “beam shearing” of optical beams across interferometer elements and the lateral shearing of reference and measurement beams one with respect to the other. Beam shearing can be caused, for example, by a change in direction of propagation of the input beam to an interferometer or a change in orientation of the object mirror in a double pass plane mirror interferometer such as a differential plane mirror interferometer (DPMI) or a high stability plane mirror interferometer (HSPMI).
Accordingly, due to errors such as the aforementioned cyclic and non-cyclic errors, the observable interference phase typically includes contributions in addition to Φ. Thus, the observable phase is more accurately expressed as{tilde over (Φ)}=Φ+ψ+ζ  (3)where ψ and ζ are the contributions due to the cyclic and non-cyclic errors, respectively.
The effect of contributions to the observable phase due to cyclic and non-cyclic errors can be reduced by quantifying these errors in each interferometer and correcting subsequent measurements with this data. Different techniques for quantifying cyclic errors are described in commonly owned U.S. Pat. No. 6,252,668, U.S. Pat. No. 6,246,481, U.S. Pat. No. 6,137,574, and U.S. patent application Ser. No. 10/287,898 entitled “INTERFEROMETRIC CYCLIC ERROR COMPENSATION” filed Nov. 5, 2002 by Henry A. Hill, the entire contents each of which are incorporated herein by reference. In order to compensate for these contributions, cyclic error compensating systems and methods can be used to determine a cyclic error function characterizing the cyclic error contribution to the observed phase. Examples of apparatus and details of methods that can be used to characterize non-cyclic errors in interferometers and interferometer components are described in U.S. patent application Ser. No. 10/366,587 entitled “CHARACTERIZATION AND COMPENSATION OF NON-CYCLIC ERRORS IN INTERFEROMETRY SYSTEMS,” to Henry A. Hill, filed on Feb. 12, 2003, the entire contents of which are incorporated herein by reference.
Assuming any contributions due to cyclic and/or non-cyclic errors are small or otherwise compensated, according to Equation (2) the observable phase measured by a displacement measuring interferometer should be equal to 2 pkL (1−θ2). This relationship assumes that the optical path difference between the measurement and reference beam is equal to 2 pkL (1−θ2) and allows one to readily determine L, a displacement of the measurement object from the interferometer, from the measured phase, provided the orientation of the measurement object is known.
In the case of an interferometric metrology system including two or more linear displacement plane mirror interferometers used, in part, to measure a change in angular orientation of a measurement object, the observable phases measured by the two or more interferometers should each be of the form 2 pkL (1−θ2). The resulting differences of phases obtained either optically or electronically can be used to compute a change in angular orientation of a measurement object common to the two or more plane mirror interferometers, provided that the measurement axes of the two or more interferometers are parallel.
The interferometers described above are often crucial components of scanner systems and stepper systems used in lithography to produce integrated circuits on semiconductor wafers. Such lithography systems typically include a translatable stage to support and fix the wafer, focusing optics used to direct a radiation beam onto the wafer, a scanner or stepper system for translating the stage relative to the exposure beam, and one or more interferometers. Each interferometer directs a measurement beam to, and receives a reflected measurement beam from, a plane mirror attached to the stage. Each interferometer interferes its reflected measurement beams with a corresponding reference beam, and collectively the interferometers accurately measure changes in the position of the stage relative to the radiation beam. The interferometers enable the lithography system to precisely control which regions of the wafer are exposed to the radiation beam.
In practice, the interferometry systems are used to measure the position of the wafer stage along multiple measurement axes. For example, defining a Cartesian coordinate system in which the wafer stage lies in the x-y plane, measurements are typically made of the x and y positions of the stage as well as the angular orientation of the stage with respect to the z axis, as the wafer stage is translated along the x-y plane. Furthermore, it may be desirable to also monitor tilts of the wafer stage out of the x-y plane. For example, accurate characterization of such tilts may be necessary to calculate Abbe offset errors in the x and y positions. Thus, depending on the desired application, there may be up to five degrees of freedom to be measured. Moreover, in some applications, it is desirable to also monitor the position of the stage with respect to the z-axis, resulting in a sixth degree of freedom.
To measure each degree of freedom, an interferometer is used to monitor distance changes along a corresponding metrology axis. For example, in systems that measure the x and y positions of the stage as well as the angular orientation of the stage with respect to the x, y, and z axes, at least three spatially separated measurement beams reflect from one side of the wafer stage and at least two spatially separated measurement beams reflect from another side of the wafer stage. See, e.g., U.S. Pat. No. 5,801,832 entitled “METHOD OF AND DEVICE FOR REPETITIVELY IMAGING A MASK PATTERN ON A SUBSTRATE USING FIVE MEASURING AXES,” the contents of which are incorporated herein by reference. Each measurement beam is recombined with a reference beam to monitor optical path length changes along the corresponding metrology axes. Because the different measurement beams contact the wafer stage at different locations, the angular orientation of the wafer stage can then be derived from appropriate combinations of the optical path length measurements. Accordingly, for each degree of freedom to be monitored, the system includes at least one measurement beam that contacts the wafer stage. Furthermore, as described above, each measurement beam may double-pass the wafer stage to prevent changes in the angular orientation of the wafer stage from corrupting the interferometric signal. The measurement beams may be generated from physically separate interferometers or from multi-axes interferometers that generate multiple measurement beams.